The government has backed proposals to give free lunches to every primary school pupil in England, although they are unlikely to become reality before the next parliament because of the cost.

The education secretary, Michael Gove, supports extending free school lunches to the 3 million primary school pupils in England who currently do not receive them. But the price tag of £900m a year puts the policy out of reach until 2016 at the very earliest, Department for Education (DfE) sources suggested.

The recommendation is one of a series of measures in the School Food Plan, a report by the co-founders of the Leon chain of restaurants, Henry Dimbleby and John Vincent, commissioned by the department.

“We understand that the considerable cost and the need to involve other departments make it a big ask. But we are pleased that the secretary of state agrees with us in principle and we would urge schools and councils to consider funding universal free school meals themselves,” Dimbleby and Vincent said.

The plan aims to improve the quality and image of school lunches among both children and parents, as well as changing the approach of teachers and schools to diet and nutrition.

Celebrity chef Jamie Oliver, who publicised the grim reality of school catering and the notorious Turkey Twizzlers in 2005, also gave his backing to the report.

“I know how much energy and passion has gone into this plan. Now it has to deliver on its promises and make sure no schools are left behind – that responsibility sits with this government,” Oliver said.

The plan said universal provision of free school meals would address rising food poverty experienced by the most disadvantaged households. The plan’s authors found that just 20% of children from the lowest-paid working families who were above the threshold to qualify for free meals bought school lunches.

The report said this was overwhelmingly because the parents – typically on a household budget of £10 a day – could not afford to pay. Instead, many children relied on nutritionally-poor packed lunches, or were going without lunch altogether. Carmel McConnell, founder of the Magic Breakfast charity, said funding was essential to help tackle food insecurity in the poorest families: “We can’t emphasize enough how important it is for children to be given nutritious food at school because, sadly, all too often there are empty cupboards at home.”

The report urged councils to follow the lead of the handful of Labour-run authorities that have pioneered universal free school meals.

Islington councillor Richard Watts said: “We feel this shows that the decision we took to go ahead with free school meals despite the massive government cuts to our budget was absolutely the right thing to do.”

In Islington, school meal takeup has soared to 82% under the scheme, against a national average of 43%. In Durham, takeup rose to 85% before its free school meal scheme was abandoned after government-imposed budget cuts.

Apart from the universal free school meals, the other recommendations made by the report have been accepted by the DfE – notably a decision by Gove to enforce national nutritional standards on academies and free schools that open next year as well as maintained schools.

That still leaves more than 2,000 existing free schools and academies outside the food guidelines, but Dimbleby said those will be asked to voluntarily include the food standards in their contracts with government.

The measure that may have the biggest impact is the announcement that Ofsted chief inspector Sir Michael Wilshaw is to include “behaviour and culture in the dining hall” in its guidelines for school inspections. Inspectors will consider “how lunchtime and the dining space contribute to good behaviour and the culture in the school,” as well as investigating what school leaders are doing to ensure a healthy diet for their pupils.

Dimbleby said he had visited and eaten at 50 schools and consulted with teachers, industry representatives and parents in the course of a year while writing the report.

The authors backed away from earlier suggestions they would call for a blanket ban on packed lunches, although they do want schools to monitor lunches brought from home, and for schools to ban sugary drinks and confectionery.

Brian Lightman, general secretary of the Association of School and College Leaders, said banning packed lunches wasn’t feasible, and that spending would be needed to avoid long queues at lunchtime.

“There needs to be significant additional investment if all schools are to be able to avoid long dinner queues and create the kind of environment that we all would like to eat in,” Lightman said.

Dimbleby urged all parents to read the report, saying he thought they should be involved in the debate and know what the options were.